My boys like BlueStacks so I was forced to learn how to deal with it when it comes time to transfer it to a new computer so they do not lose their game levels, etc. The typical thing to do is to create a backup via their settings but every time we try to that we get some error message about the backup could not be created. If you get this issue too then read on. The best thing to do is transfer the whole folder that has the BlueStacks data to the new computer. You do this by locating ProgramData which is a hidden folder under C: of Windows. If you do not see that folder under C: then you need to enable view hidden files from the top portion of Explorer. Within ProgramData is a file called "BlueStacks" which you can now copy over to the new hard drive and replace with the new installation of BlueStacks in the same location of the "ProgramData" on the new drive.
I was hoping for more on how to transfer bluestacks files to new drive this needs looking into soon so as to find how to transfer bluestacks what and maybe get a better idea.